Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique
The present study investigates different types of wave symmetries in the (3+1)\left(3+1)-dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons, periodic cross kink, multiple waves, mixed wa...
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De Gruyter
2025-07-01
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| Series: | Open Physics |
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| Online Access: | https://doi.org/10.1515/phys-2025-0176 |
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| author | Ceesay Baboucarr Baber Muhammad Z. Ahmed Nauman Shahid Naveed Macías Siegfried Macías-Díaz Jorge E. |
| author_facet | Ceesay Baboucarr Baber Muhammad Z. Ahmed Nauman Shahid Naveed Macías Siegfried Macías-Díaz Jorge E. |
| author_sort | Ceesay Baboucarr |
| collection | DOAJ |
| description | The present study investigates different types of wave symmetries in the (3+1)\left(3+1)-dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons, periodic cross kink, multiple waves, mixed waves, homoclinic breathers, M-shaped related waves and periodic lump waves. These solutions exhibit stability, energy confinement, and dynamic interactions. It is observed that the Hirota method captures the highly nonlinear complex phenomena that result from the balance between the nonlinearity and the dispersion. These factors lead to a stability and coherent formation of wave forms. We employed Mathematica 11.1 software to obtain 3D, contour, and 2D graphs of our solution. The graphs present the spatial and temporal evolution of these solutions. The periodic structures, oscillatory solitons, and cross-kink configurations have dynamic interaction while maintaining fundamental properties of waves. Breather and homoclinic breather solutions present the basis of oscillatory local dynamics, which stress on energy transfer and phase modulation. The novelty of this article is in the use of the Hirota bilinear technique to the Chafee–Infante equation in (3+1)\left(3+1)-dimensional dimension, which allows the derivation of a wide variety of exact multidimensional wave solutions, including intricate hybrid solutions previously unreported for the equation. This provides great value by extending the analytical theory and improving the understanding of nonlinear wave behaviors in high-dimensional environments. It is worth noting that all the solutions have been verified and found to satisfy the governing equation. |
| format | Article |
| id | doaj-art-7e81bbfeaa1a429b8bde9eda1066a276 |
| institution | Kabale University |
| issn | 2391-5471 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Physics |
| spelling | doaj-art-7e81bbfeaa1a429b8bde9eda1066a2762025-08-20T03:28:13ZengDe GruyterOpen Physics2391-54712025-07-01231102110.1515/phys-2025-0176Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation techniqueCeesay Baboucarr0Baber Muhammad Z.1Ahmed Nauman2Shahid Naveed3Macías Siegfried4Macías-Díaz Jorge E.5Department of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Sargodha Campus, Sargodha, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Statistics, The University of Lahore, Lahore, PakistanDepartment of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes, MexicoDepartment of Mathematics and Physics, Autonomous University of Aguascalientes, Aguascalientes, MexicoThe present study investigates different types of wave symmetries in the (3+1)\left(3+1)-dimensional Chafee–Infante equation via the Hirota bilinear transformation technique. In this work, we derived exact solutions that include bright and dark solitons, periodic cross kink, multiple waves, mixed waves, homoclinic breathers, M-shaped related waves and periodic lump waves. These solutions exhibit stability, energy confinement, and dynamic interactions. It is observed that the Hirota method captures the highly nonlinear complex phenomena that result from the balance between the nonlinearity and the dispersion. These factors lead to a stability and coherent formation of wave forms. We employed Mathematica 11.1 software to obtain 3D, contour, and 2D graphs of our solution. The graphs present the spatial and temporal evolution of these solutions. The periodic structures, oscillatory solitons, and cross-kink configurations have dynamic interaction while maintaining fundamental properties of waves. Breather and homoclinic breather solutions present the basis of oscillatory local dynamics, which stress on energy transfer and phase modulation. The novelty of this article is in the use of the Hirota bilinear technique to the Chafee–Infante equation in (3+1)\left(3+1)-dimensional dimension, which allows the derivation of a wide variety of exact multidimensional wave solutions, including intricate hybrid solutions previously unreported for the equation. This provides great value by extending the analytical theory and improving the understanding of nonlinear wave behaviors in high-dimensional environments. It is worth noting that all the solutions have been verified and found to satisfy the governing equation.https://doi.org/10.1515/phys-2025-0176(3+1)-dimensional chafee–infante equationhirota bilinear methodsoliton solutionsm-shaped wavesbreather waveslump solutionsrogue waveskink and anti-kink structureswave interactionnonlinear wave dynamicsmultidimensional solitonsperiodic cross-kinksexact analytical solutions |
| spellingShingle | Ceesay Baboucarr Baber Muhammad Z. Ahmed Nauman Shahid Naveed Macías Siegfried Macías-Díaz Jorge E. Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique Open Physics (3+1)-dimensional chafee–infante equation hirota bilinear method soliton solutions m-shaped waves breather waves lump solutions rogue waves kink and anti-kink structures wave interaction nonlinear wave dynamics multidimensional solitons periodic cross-kinks exact analytical solutions |
| title | Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique |
| title_full | Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique |
| title_fullStr | Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique |
| title_full_unstemmed | Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique |
| title_short | Abundant wave symmetries in the (3+1)-dimensional Chafee–Infante equation through the Hirota bilinear transformation technique |
| title_sort | abundant wave symmetries in the 3 1 dimensional chafee infante equation through the hirota bilinear transformation technique |
| topic | (3+1)-dimensional chafee–infante equation hirota bilinear method soliton solutions m-shaped waves breather waves lump solutions rogue waves kink and anti-kink structures wave interaction nonlinear wave dynamics multidimensional solitons periodic cross-kinks exact analytical solutions |
| url | https://doi.org/10.1515/phys-2025-0176 |
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